• Communications of Mathematical Education
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• v.24 no.1
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• pp.235-257
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• 2010

Contemporary belief is that the creative talented can create new knowledge and lead national development, so lots of countries in the world have interest in Gifted Education. As we well know, U.S.A., England, Russia, Germany, Australia, Israel, and Singapore enforce related laws in Gifted Education to offer Gifted Classes, and our government has also created an Improvement Act in January, 2000 and Enforcement Ordinance for Gifted Improvement Act was also announced in April, 2002. Through this initiation Gifted Education can be possible. Enforcement Ordinance was revised in October, 2008. The main purpose of this revision was to expand the opportunity of Gifted Education to students with special education needs. One of these programs is, the opportunity of Gifted Education to be offered to lots of the Gifted by establishing Special Classes at each school. Also, it is important that the quality of Gifted Education should be combined with the expansion of opportunity for the Gifted. Social opinion is that it will be reckless only to expand the opportunity for the Gifted Education, therefore, assessment on the Teaching and Learning Program for the Gifted is indispensible. In this study, 3 middle schools were selected for the Teaching and Learning Programs in mathematics. Each 1st Grade was reviewed and analyzed through comparative tables between Regular and Gifted Education Programs. Also reviewed was the content of what should be taught, and programs were evaluated on assessment standards which were revised and modified from the present teaching and learning programs in mathematics. Below, research issues were set up to assess the formation of content areas and appropriateness for Teaching and Learning Programs for the Gifted in mathematics. A. Is the formation of special class content areas complying with the 7th national curriculum? 1. Which content areas of regular curriculum is applied in this program? 2. Among Enrichment and Selection in Curriculum for the Gifted, which one is applied in this programs? 3. Are the content areas organized and performed properly? B. Are the Programs for the Gifted appropriate? 1. Are the Educational goals of the Programs aligned with that of Gifted Education in mathematics? 2. Does the content of each program reflect characteristics of mathematical Gifted students and express their mathematical talents? 3. Are Teaching and Learning models and methods diverse enough to express their talents? 4. Can the assessment on each program reflect the Learning goals and content, and enhance Gifted students' thinking ability? The conclusions are as follows: First, the best contents to be taught to the mathematical Gifted were found to be the Numeration, Arithmetic, Geometry, Measurement, Probability, Statistics, Letter and Expression. Also, Enrichment area and Selection area within the curriculum for the Gifted were offered in many ways so that their Giftedness could be fully enhanced. Second, the educational goals of Teaching and Learning Programs for the mathematical Gifted students were in accordance with the directions of mathematical education and philosophy. Also, it reflected that their research ability was successful in reaching the educational goals of improving creativity, thinking ability, problem-solving ability, all of which are required in the set curriculum. In order to accomplish the goals, visualization, symbolization, phasing and exploring strategies were used effectively. Many different of lecturing types, cooperative learning, discovery learning were applied to accomplish the Teaching and Learning model goals. For Teaching and Learning activities, various strategies and models were used to express the students' talents. These activities included experiments, exploration, application, estimation, guess, discussion (conjecture and refutation) reconsideration and so on. There were no mention to the students about evaluation and paper exams. While the program activities were being performed, educational goals and assessment methods were reflected, that is, products, performance assessment, and portfolio were mainly used rather than just paper assessment.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.313-330
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• 2015

The classification is an important activity that is directly related to concept formation. Thus it will need to be made meaningful learning to classification through learner-centered teaching. But we doubts weather teaching and learning to the classification are reflected in the constructivist philosophy of 'learner-centered' well or not. The purpose of this study was to analyze critically the content of elementary textbooks and guidebook for teachers relating to the classification of angles and triangles in terms of constructivism. As a result, there is a problem in the classification of angles that are not provided a reasonable chance to set criteria by agreement of the communities. There is a problem in the classification of triangles that has the characteristics of radical development in terms of diversity. In addition, response of students was predicted like anyone who already acquired knowledge. And it has the shortcomings that the opportunity to have a choice and a discussion to hierarchical and partition classification are not provided. The followings are proposed based on such features; faithful reflection of 'Learner-centered' principle, careful prediction of student response, teaching that focus on process than results.

• Journal for History of Mathematics
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• v.33 no.6
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• pp.327-343
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• 2020

This study investigate philosophical discussions related to the Zeno's paradoxes in order to derive the mathematics educational implications. The paradox of Zeno's motion is sometimes explained by the calculus theories. However, various philosophical discussions show that the resolution of Zeno's paradox by calculus is not a real solution, and the concept of a continuum which is composed of points and the real number continuum may not coincide with the physical space and time. This is supported by the fact that the hyperreal number system of nonstandard analysis could be another model of a straight line or time and that an alternative explanation of Zeno's paradox was possible by the hyperreal number system. The existence of two different theories of the continuum suggests that teachers and students may not have the same view of the continuum. It is also suggested that the real world model used in school mathematics may not necessarily match the student's intuition or mathematical practice, and that the real world application of mathematics theory should be emphasized in education as a kind of 'correspondence.'

• Journal of the Korean Society of Earth Science Education
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• v.15 no.3
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• pp.354-372
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• 2022

The purpose of this study is to explore the philosophical position of various scientific theories based on the scientific worldviews for science education. In addition, it aims to expand science education, which has usually dealt with epistemology and methodology, to ontology, that is, to the problem of metaphysics. It can be said that there exists a physical realism, traditionally defined as a strong determinism of the metaphysical belief. That is fixed and unchanging objective scientific knowledge independent of our minds, which was established by Newton, Einstein and Schridinger. What can be seen in the natural laws of dynamics can be called 'mathematicization'. Einstein also shook the traditional views to some extent through the theory of relativity, but his theory was still close to traditional thinking. On the contrary, to escape from this rigid determinism, we need anthropomorphic concepts such as 'possibility' and 'chance'. It is a characteristic of the modern scientific worldviews that leads the change of scientific theory from a classically strong deterministic thought to a weak deterministic accidental accident, probability theory, and a naturalistic point of view. This can be said to correspond to Darwin's theory of evolution and quantum mechanics. We can have three types of epistemological worlds that justify this ontological worldviews. These are rationalism, empiricism and naturalism. In many cases, science education does not tell us what kind of metaphysical beliefs the scientific theories we deal with in the field of education are based on. Also, science education focuses only on the understanding of scientific knowledge. However, it can be said that true knowledge can bring understanding only when it is connected to the knowledge of learned knowledge and the learner's own metaphysical belief in the world. Therefore, in the future, science education needs to connect various scientific theories based on scientific worldviews and philosophical position and present them to students.

• Journal of the Korean Society of Earth Science Education
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• v.15 no.2
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• pp.158-170
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• 2022

The purpose of this study is to understand the characteristics of Aristotle's view of nature that is, the static view of the universe, and find implications for education. Plato sought to interpret the natural world using a rational approach rather than an incomplete observation, in terms of from the perspective of geometry and mathematical regularity, as the best way to understand the world. On the other hand, Aristotle believed that we could understand the world by observing what we see. This world is a static worldview full of the purpose of the individual with a sense of purposive legitimacy. In addition, the natural motion of earthly objects and celestial bodies, which are natural movements towards the world of order, are the original actions. Aristotle thought that, given the opportunity, all natural things would carry out some movement, that is, their natural movement. Above all, the world that Plato and Aristotle built is a static universe. It is possible to fully grasp the world by approaching the objective nature that exists independently of human being with human reason and observation. After all, for Aristotle, like Plato, their belief that the natural world was subject to regular and orderly laws of nature, despite the complexity of what seemed to be an embarrassingly continual change, became the basis of Western thought. Since the universe, the metaphysical perspective of ancient Greece and modern philosophy, relies on the development of a dichotomy of understanding (cutting branches) into what has already been completed or planned, ideal and inevitable, so it is the basis of traditional teaching-learning that does not value learner's opinions.